Uncertainty Quantification for the Extended and the Deterministic-Gain Kalman Filters

This paper is aimed at characterizing the mean square error and probabilistic uncertainty of a popular class of filtering algorithms in nonlinear systems. The state estimation error of the extended Kalman filter and the deterministic-gain Kalman filter are analyzed. We allow a vector state, but assume scalar measurements. A set of conditions for the mean square error to be upper-bounded is derived. Furthermore, the probabilistic bounds for the estimation error are computed via both the moment-based approach and the stochastic comparison analysis approach. The latter provides a formal means determining uncertainty bounds, such as statistical confidence regions.